CAGR from an equity curve

easyFinanceacceptance —~10 min

Implement cagr(equity, periods_per_year) — the compound annual growth rate of an equity curve sampled once per period: (last / first) ** (periods_per_year / (n - 1)) - 1, where n is the number of samples.

A backtest that doubled looks different over two years than over ten. CAGR is how the portfolio page annualises a curve of any length. Return the rate rounded to 4 decimal places.

example 1

input

equity=[100.0, 101.0, 103.0, 102.5, 104.0, 106.0], periods_per_year=252

output

17.8545

example 2

input

equity=[100.0, 104.0, 103.0, 108.0, 110.0, 112.0, 115.0], periods_per_year=12

output

0.3225

constraints

2 ≤ n ≤ 10_000
every value > 0
periods_per_year ∈ {12, 52, 252}

teacher · 2 hints · the first is free

↗ read the theory

the chapter this problem is cut from

●solution.py· utf-8 · spaces:4

def cagr(equity: list, periods_per_year: int) -> float:
    """Annualised growth of an equity curve, rounded to 4 dp."""
    periods = len(equity) - 1
    # TODO: the curve is not always daily — use periods_per_year
    return round((equity[-1] / equity[0]) ** (252 / periods) - 1, 4)

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python 3.13 · pyodide

+ 6 hidden on submit

input · keyword arguments to cagr()

equity=[100.0, 101.0, 103.0, 102.5, 104.0, 106.0], periods_per_year=252

expected

17.8545

the judge calls cagr() with exactly these inputs · outputs are compared to 6 decimal places

● standing bypython 3.13 in your browser · pyodide 0.28.3 · judged on the server to 6 dp⌘↵ run · ⌘⇧↵ submit

paper only · educational · not advice